And we, as as species, for hundreds of years have decided to call them number too, so 0.5 is a number

Have you ever heard of real numbers? Irrational numbers?

And a quotient, by definition, is "the number we obtain by dividing a number by another"

And the elements of a set of number ("all the numbers between 0 and 1" is a set of numbers, right?) are called...?

Does it extends to number above 1? 2.25 and 2.75 are not different number?

So 1/4, or 0.25, is not different from 3/4, or 0.75? Or are you saying that 0.25 and 0.75 are not numbers at all?

A fraction is a numeral which represent a rational number. It is composed by a numerator and a denominator.

Fractions are another way to represent finite and infinite decimal numbers

As someone said, numbers are not pies. It's like you are trying to demolish hundreds of years of maths by saying that fractions are not different numbers ahah

0.1 is 1/10, a portion out of 10 of 1. 0.2 is 2/10, two portion out of 10 of 1. 0.1 and 0.2 are two different number.

Or am I misinterpreting something?

It doesn't say this, op doesn't specify real, natural or whatever set of number even though by same "number from one to zero" we can think of fraction and irrational number

Are you saying that 0.1 and 0.2 are not different numbers?